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A Hierarchy of Cameras

This allows us to define a hierarchy of camera designs, where the order is determined by the stability and complexity of the computations necessary to estimate structure and motion. The dioptric axis (number and spacing of view points) determines if the 3D motion estimation is scene-independent or scene-independent and the field of view axis determines the noise sensitivity of the estimation. At the low end of this hierarchy is the standard planar pinhole camera for which the structure from motion problem is scene dependent and ill-posed. At the high end is a camera , which we call the full field of view polydioptric camera, for which the problem is scene independent and stable. In between are multiple view cameras with a large field of view which we have built, as well as catadioptric panoramic sensors and other omni-directional cameras. This classification is summarized in the following two figures:

A hierarchy of camera designs.

Hierarchy for Moving Camera - Static World	Hierarchy for Moving Object - Static Cameras
Small Field of View Pinhole Cameras.
Small Field of View Pinhole Camera	Small Field of View Stereo Camera
At the bottom of the camera hierarchy is the standard smalll field of view pinhole camera. Pinhole cameras capture only rays through a single point in space. This makes it impossible to apply the plenoptic motion constraint unless the motion consists of pure rotation. We need to estimate both the camera motion and the scene structure which leads to a non-linear problem. Since the stability of the problem depends on the field of view and conventional cameras have a rather small field this estimation is also very noise sensitive.
Spherical Pinhole Camera and its Argus Eye Implementation
Spherical Pinhole Camera (Omnidirectional Camera)	Multiple Small Field of View Pinhole Cameras (Argus Eye)
Higher in the hierarchy along the field of view axis, we find the large field of view pinhole cameras. Under the term Omni-directional vision these cameras have been subject of intense studies recently. For some example research groups who study these cameras see the Page of Omnidirectional Vision. If we disregard the problems of the often non-planar signal processing, the scene structure and 3D motion estimation for these large field of view cameras becomes well-posed and stable. Nevertheless, due to the single view point the scene and motion parameters are still couples, causing the estimation to be nonlinear.
Polydioptric Cameras
Plenoptic Manifold Camera	Spherical Polydioptric Camera
A polydioptric camera is a generalized camera that captures a multi-perspective subset of the space of light rays. An example implementation would be a regular array of many closely spaced conventional pinhole cameras. This cameras allows us to apply the plenoptic motion constraints which decouples the estimation of camera motion and scene structure, thus greatly simplifying the estimation of either one. These stability of the 3D motion estimation still depends on teh field of view of the camera, thus suggesting that the optimal camera for 3D motion estimation would be a spherical field of view polydioptric camera.
Multi View Stereo and Polydioptric Domes
Multi View Stereo Dome	Multi View Plenoptic Dome
The presented classification of cameras applies also to camera arrangements where the cameras surround the object of interest. If the object is surrounded from all sides by conventional pinhole cameras then the object shape and motion estimation is well-posed, but non-linear For an example click here. If the pinhole cameras are replaced with polydioptric cameras, then the shape and motion estimation becomes linear.